After sufficiently long times, most thermal interacting systems will eventually settle into a state of thermodynamic equilibrium. Hydrodynamics is a universal framework that describes such systems, organizing the dynamics of conserved charges in terms of a gradient expansion of slowly varying fluxes that are constrained to obey local versions of the first and second laws of thermodynamics. Intuitively, if the equilibrium state is stable, then collective hydrodynamic excitations should decay exponentially with time. I will discuss recent work showing that, within the linearized regime, the local laws of thermodynamics guarantee that this will be the case. In fact, the converse is true as well—if there is a linear instability in the system, then there must be a thermodynamic instability as well. I will end with a few examples in systems with spontaneously broken global symmetries where long-known “Landau instabilities” are reframed as thermodynamic instabilities.

A talk within the Pacific Northwest Particle Theory Seminar.